Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(132.316651346\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 229 x^{7} + 267 x^{6} + 16434 x^{5} - 16568 x^{4} - 405504 x^{3} + 202288 x^{2} + \cdots + 1190400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 5^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(6.71211\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.71211 | −1.18655 | −0.593273 | − | 0.805002i | \(-0.702164\pi\) | ||||
−0.593273 | + | 0.805002i | \(0.702164\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 13.0525 | 0.407889 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −60.4090 | −0.685052 | ||||||||
\(7\) | 177.172 | 1.36663 | 0.683314 | − | 0.730124i | \(-0.260538\pi\) | ||||
0.683314 | + | 0.730124i | \(0.260538\pi\) | |||||||
\(8\) | 127.178 | 0.702566 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 117.472 | 0.235495 | ||||||||
\(13\) | 783.433 | 1.28571 | 0.642856 | − | 0.765987i | \(-0.277749\pi\) | ||||
0.642856 | + | 0.765987i | \(0.277749\pi\) | |||||||
\(14\) | −1189.20 | −1.62157 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1271.31 | −1.24152 | ||||||||
\(17\) | 1335.12 | 1.12047 | 0.560233 | − | 0.828335i | \(-0.310711\pi\) | ||||
0.560233 | + | 0.828335i | \(0.310711\pi\) | |||||||
\(18\) | −543.681 | −0.395515 | ||||||||
\(19\) | −915.496 | −0.581798 | −0.290899 | − | 0.956754i | \(-0.593954\pi\) | ||||
−0.290899 | + | 0.956754i | \(0.593954\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1594.55 | 0.789023 | ||||||||
\(22\) | 812.166 | 0.357757 | ||||||||
\(23\) | 1684.59 | 0.664011 | 0.332006 | − | 0.943277i | \(-0.392275\pi\) | ||||
0.332006 | + | 0.943277i | \(0.392275\pi\) | |||||||
\(24\) | 1144.60 | 0.405627 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5258.49 | −1.52555 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 2312.53 | 0.557433 | ||||||||
\(29\) | 1720.16 | 0.379817 | 0.189909 | − | 0.981802i | \(-0.439181\pi\) | ||||
0.189909 | + | 0.981802i | \(0.439181\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7741.92 | 1.44692 | 0.723460 | − | 0.690366i | \(-0.242551\pi\) | ||||
0.723460 | + | 0.690366i | \(0.242551\pi\) | |||||||
\(32\) | 4463.49 | 0.770548 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | −8961.50 | −1.32948 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1057.25 | 0.135963 | ||||||||
\(37\) | 9013.63 | 1.08242 | 0.541209 | − | 0.840888i | \(-0.317967\pi\) | ||||
0.541209 | + | 0.840888i | \(0.317967\pi\) | |||||||
\(38\) | 6144.91 | 0.690330 | ||||||||
\(39\) | 7050.90 | 0.742306 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13835.8 | 1.28542 | 0.642710 | − | 0.766109i | \(-0.277810\pi\) | ||||
0.642710 | + | 0.766109i | \(0.277810\pi\) | |||||||
\(42\) | −10702.8 | −0.936212 | ||||||||
\(43\) | −11885.9 | −0.980307 | −0.490153 | − | 0.871636i | \(-0.663059\pi\) | ||||
−0.490153 | + | 0.871636i | \(0.663059\pi\) | |||||||
\(44\) | −1579.35 | −0.122983 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −11307.2 | −0.787880 | ||||||||
\(47\) | 20567.8 | 1.35814 | 0.679068 | − | 0.734075i | \(-0.262384\pi\) | ||||
0.679068 | + | 0.734075i | \(0.262384\pi\) | |||||||
\(48\) | −11441.8 | −0.716789 | ||||||||
\(49\) | 14583.0 | 0.867673 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12016.1 | 0.646902 | ||||||||
\(52\) | 10225.7 | 0.524428 | ||||||||
\(53\) | 3483.63 | 0.170350 | 0.0851750 | − | 0.996366i | \(-0.472855\pi\) | ||||
0.0851750 | + | 0.996366i | \(0.472855\pi\) | |||||||
\(54\) | −4893.13 | −0.228351 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 22532.4 | 0.960147 | ||||||||
\(57\) | −8239.46 | −0.335901 | ||||||||
\(58\) | −11545.9 | −0.450670 | ||||||||
\(59\) | −22223.3 | −0.831147 | −0.415574 | − | 0.909560i | \(-0.636419\pi\) | ||||
−0.415574 | + | 0.909560i | \(0.636419\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −40834.7 | −1.40509 | −0.702546 | − | 0.711638i | \(-0.747954\pi\) | ||||
−0.702546 | + | 0.711638i | \(0.747954\pi\) | |||||||
\(62\) | −51964.6 | −1.71684 | ||||||||
\(63\) | 14350.9 | 0.455543 | ||||||||
\(64\) | 10722.5 | 0.327225 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7309.49 | 0.206551 | ||||||||
\(67\) | −2692.02 | −0.0732640 | −0.0366320 | − | 0.999329i | \(-0.511663\pi\) | ||||
−0.0366320 | + | 0.999329i | \(0.511663\pi\) | |||||||
\(68\) | 17426.6 | 0.457026 | ||||||||
\(69\) | 15161.3 | 0.383367 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13211.7 | 0.311039 | 0.155519 | − | 0.987833i | \(-0.450295\pi\) | ||||
0.155519 | + | 0.987833i | \(0.450295\pi\) | |||||||
\(72\) | 10301.4 | 0.234189 | ||||||||
\(73\) | 37232.0 | 0.817728 | 0.408864 | − | 0.912595i | \(-0.365925\pi\) | ||||
0.408864 | + | 0.912595i | \(0.365925\pi\) | |||||||
\(74\) | −60500.5 | −1.28434 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11949.5 | −0.237309 | ||||||||
\(77\) | −21437.8 | −0.412054 | ||||||||
\(78\) | −47326.4 | −0.880779 | ||||||||
\(79\) | −46277.2 | −0.834257 | −0.417128 | − | 0.908848i | \(-0.636963\pi\) | ||||
−0.417128 | + | 0.908848i | \(0.636963\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −92867.6 | −1.52521 | ||||||||
\(83\) | −401.818 | −0.00640227 | −0.00320113 | − | 0.999995i | \(-0.501019\pi\) | ||||
−0.00320113 | + | 0.999995i | \(0.501019\pi\) | |||||||
\(84\) | 20812.8 | 0.321834 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 79779.7 | 1.16318 | ||||||||
\(87\) | 15481.5 | 0.219288 | ||||||||
\(88\) | −15388.5 | −0.211832 | ||||||||
\(89\) | −33472.8 | −0.447937 | −0.223969 | − | 0.974596i | \(-0.571901\pi\) | ||||
−0.223969 | + | 0.974596i | \(0.571901\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 138803. | 1.75709 | ||||||||
\(92\) | 21988.1 | 0.270843 | ||||||||
\(93\) | 69677.3 | 0.835380 | ||||||||
\(94\) | −138053. | −1.61149 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 40171.4 | 0.444876 | ||||||||
\(97\) | −168527. | −1.81861 | −0.909305 | − | 0.416130i | \(-0.863386\pi\) | ||||
−0.909305 | + | 0.416130i | \(0.863386\pi\) | |||||||
\(98\) | −97882.6 | −1.02953 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 176215. | 1.71885 | 0.859425 | − | 0.511261i | \(-0.170821\pi\) | ||||
0.859425 | + | 0.511261i | \(0.170821\pi\) | |||||||
\(102\) | −80653.5 | −0.767578 | ||||||||
\(103\) | 66485.7 | 0.617497 | 0.308749 | − | 0.951144i | \(-0.400090\pi\) | ||||
0.308749 | + | 0.951144i | \(0.400090\pi\) | |||||||
\(104\) | 99635.5 | 0.903297 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −23382.5 | −0.202128 | ||||||||
\(107\) | −87124.1 | −0.735663 | −0.367831 | − | 0.929892i | \(-0.619900\pi\) | ||||
−0.367831 | + | 0.929892i | \(0.619900\pi\) | |||||||
\(108\) | 9515.24 | 0.0784983 | ||||||||
\(109\) | 17894.5 | 0.144263 | 0.0721314 | − | 0.997395i | \(-0.477020\pi\) | ||||
0.0721314 | + | 0.997395i | \(0.477020\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 81122.7 | 0.624935 | ||||||||
\(112\) | −225241. | −1.69669 | ||||||||
\(113\) | 32973.4 | 0.242922 | 0.121461 | − | 0.992596i | \(-0.461242\pi\) | ||||
0.121461 | + | 0.992596i | \(0.461242\pi\) | |||||||
\(114\) | 55304.2 | 0.398562 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 22452.4 | 0.154923 | ||||||||
\(117\) | 63458.1 | 0.428570 | ||||||||
\(118\) | 149165. | 0.986194 | ||||||||
\(119\) | 236547. | 1.53126 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 274087. | 1.66721 | ||||||||
\(123\) | 124522. | 0.742138 | ||||||||
\(124\) | 101051. | 0.590183 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −96325.2 | −0.540522 | ||||||||
\(127\) | −297307. | −1.63567 | −0.817836 | − | 0.575451i | \(-0.804826\pi\) | ||||
−0.817836 | + | 0.575451i | \(0.804826\pi\) | |||||||
\(128\) | −214803. | −1.15882 | ||||||||
\(129\) | −106973. | −0.565980 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 44531.9 | 0.226722 | 0.113361 | − | 0.993554i | \(-0.463838\pi\) | ||||
0.113361 | + | 0.993554i | \(0.463838\pi\) | |||||||
\(132\) | −14214.1 | −0.0710044 | ||||||||
\(133\) | −162200. | −0.795102 | ||||||||
\(134\) | 18069.1 | 0.0869310 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 169798. | 0.787202 | ||||||||
\(137\) | −193093. | −0.878953 | −0.439476 | − | 0.898254i | \(-0.644836\pi\) | ||||
−0.439476 | + | 0.898254i | \(0.644836\pi\) | |||||||
\(138\) | −101765. | −0.454882 | ||||||||
\(139\) | −45294.3 | −0.198841 | −0.0994206 | − | 0.995046i | \(-0.531699\pi\) | ||||
−0.0994206 | + | 0.995046i | \(0.531699\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 185110. | 0.784120 | ||||||||
\(142\) | −88678.7 | −0.369061 | ||||||||
\(143\) | −94795.4 | −0.387657 | ||||||||
\(144\) | −102976. | −0.413839 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −249905. | −0.970271 | ||||||||
\(147\) | 131247. | 0.500951 | ||||||||
\(148\) | 117650. | 0.441507 | ||||||||
\(149\) | −461266. | −1.70210 | −0.851051 | − | 0.525083i | \(-0.824034\pi\) | ||||
−0.851051 | + | 0.525083i | \(0.824034\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −356514. | −1.27243 | −0.636216 | − | 0.771511i | \(-0.719501\pi\) | ||||
−0.636216 | + | 0.771511i | \(0.719501\pi\) | |||||||
\(152\) | −116431. | −0.408752 | ||||||||
\(153\) | 108145. | 0.373489 | ||||||||
\(154\) | 143893. | 0.488921 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 92031.5 | 0.302779 | ||||||||
\(157\) | 92075.8 | 0.298124 | 0.149062 | − | 0.988828i | \(-0.452375\pi\) | ||||
0.149062 | + | 0.988828i | \(0.452375\pi\) | |||||||
\(158\) | 310618. | 0.989883 | ||||||||
\(159\) | 31352.7 | 0.0983517 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 298463. | 0.907457 | ||||||||
\(162\) | −44038.2 | −0.131838 | ||||||||
\(163\) | 497333. | 1.46615 | 0.733074 | − | 0.680149i | \(-0.238085\pi\) | ||||
0.733074 | + | 0.680149i | \(0.238085\pi\) | |||||||
\(164\) | 180591. | 0.524309 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2697.05 | 0.00759658 | ||||||||
\(167\) | 292934. | 0.812792 | 0.406396 | − | 0.913697i | \(-0.366785\pi\) | ||||
0.406396 | + | 0.913697i | \(0.366785\pi\) | |||||||
\(168\) | 202792. | 0.554341 | ||||||||
\(169\) | 242474. | 0.653054 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −74155.1 | −0.193933 | ||||||||
\(172\) | −155141. | −0.399857 | ||||||||
\(173\) | −446012. | −1.13300 | −0.566502 | − | 0.824060i | \(-0.691704\pi\) | ||||
−0.566502 | + | 0.824060i | \(0.691704\pi\) | |||||||
\(174\) | −103913. | −0.260195 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 153829. | 0.374331 | ||||||||
\(177\) | −200009. | −0.479863 | ||||||||
\(178\) | 224673. | 0.531498 | ||||||||
\(179\) | −414071. | −0.965922 | −0.482961 | − | 0.875642i | \(-0.660439\pi\) | ||||
−0.482961 | + | 0.875642i | \(0.660439\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −560334. | −1.27131 | −0.635654 | − | 0.771974i | \(-0.719269\pi\) | ||||
−0.635654 | + | 0.771974i | \(0.719269\pi\) | |||||||
\(182\) | −931658. | −2.08487 | ||||||||
\(183\) | −367512. | −0.811230 | ||||||||
\(184\) | 214243. | 0.466512 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −467682. | −0.991216 | ||||||||
\(187\) | −161550. | −0.337833 | ||||||||
\(188\) | 268460. | 0.553969 | ||||||||
\(189\) | 129159. | 0.263008 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 720559. | 1.42918 | 0.714589 | − | 0.699545i | \(-0.246614\pi\) | ||||
0.714589 | + | 0.699545i | \(0.246614\pi\) | |||||||
\(192\) | 96502.7 | 0.188924 | ||||||||
\(193\) | 432118. | 0.835044 | 0.417522 | − | 0.908667i | \(-0.362899\pi\) | ||||
0.417522 | + | 0.908667i | \(0.362899\pi\) | |||||||
\(194\) | 1.13117e6 | 2.15786 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 190344. | 0.353915 | ||||||||
\(197\) | −786560. | −1.44400 | −0.721998 | − | 0.691895i | \(-0.756776\pi\) | ||||
−0.721998 | + | 0.691895i | \(0.756776\pi\) | |||||||
\(198\) | 65785.4 | 0.119252 | ||||||||
\(199\) | 284214. | 0.508761 | 0.254380 | − | 0.967104i | \(-0.418129\pi\) | ||||
0.254380 | + | 0.967104i | \(0.418129\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −24228.1 | −0.0422990 | ||||||||
\(202\) | −1.18277e6 | −2.03949 | ||||||||
\(203\) | 304765. | 0.519069 | ||||||||
\(204\) | 156840. | 0.263864 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −446259. | −0.732688 | ||||||||
\(207\) | 136452. | 0.221337 | ||||||||
\(208\) | −995988. | −1.59623 | ||||||||
\(209\) | 110775. | 0.175419 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.03608e6 | 1.60209 | 0.801045 | − | 0.598604i | \(-0.204278\pi\) | ||||
0.801045 | + | 0.598604i | \(0.204278\pi\) | |||||||
\(212\) | 45469.9 | 0.0694840 | ||||||||
\(213\) | 118906. | 0.179578 | ||||||||
\(214\) | 584787. | 0.872897 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 92712.8 | 0.135209 | ||||||||
\(217\) | 1.37165e6 | 1.97740 | ||||||||
\(218\) | −120110. | −0.171174 | ||||||||
\(219\) | 335088. | 0.472116 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.04598e6 | 1.44060 | ||||||||
\(222\) | −544504. | −0.741513 | ||||||||
\(223\) | −1.13339e6 | −1.52622 | −0.763110 | − | 0.646269i | \(-0.776328\pi\) | ||||
−0.763110 | + | 0.646269i | \(0.776328\pi\) | |||||||
\(224\) | 790807. | 1.05305 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −221321. | −0.288238 | ||||||||
\(227\) | 681222. | 0.877453 | 0.438727 | − | 0.898621i | \(-0.355430\pi\) | ||||
0.438727 | + | 0.898621i | \(0.355430\pi\) | |||||||
\(228\) | −107545. | −0.137011 | ||||||||
\(229\) | −620686. | −0.782137 | −0.391069 | − | 0.920361i | \(-0.627895\pi\) | ||||
−0.391069 | + | 0.920361i | \(0.627895\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −192941. | −0.237899 | ||||||||
\(232\) | 218767. | 0.266847 | ||||||||
\(233\) | 31388.4 | 0.0378774 | 0.0189387 | − | 0.999821i | \(-0.493971\pi\) | ||||
0.0189387 | + | 0.999821i | \(0.493971\pi\) | |||||||
\(234\) | −425938. | −0.508518 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −290068. | −0.339016 | ||||||||
\(237\) | −416495. | −0.481658 | ||||||||
\(238\) | −1.58773e6 | −1.81691 | ||||||||
\(239\) | −195859. | −0.221794 | −0.110897 | − | 0.993832i | \(-0.535372\pi\) | ||||
−0.110897 | + | 0.993832i | \(0.535372\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.33370e6 | −1.47916 | −0.739578 | − | 0.673071i | \(-0.764975\pi\) | ||||
−0.739578 | + | 0.673071i | \(0.764975\pi\) | |||||||
\(242\) | −98272.0 | −0.107868 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −532993. | −0.573122 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −835808. | −0.880580 | ||||||||
\(247\) | −717229. | −0.748024 | ||||||||
\(248\) | 984602. | 1.01656 | ||||||||
\(249\) | −3616.36 | −0.00369635 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −98131.5 | −0.0983160 | −0.0491580 | − | 0.998791i | \(-0.515654\pi\) | ||||
−0.0491580 | + | 0.998791i | \(0.515654\pi\) | |||||||
\(252\) | 187315. | 0.185811 | ||||||||
\(253\) | −203836. | −0.200207 | ||||||||
\(254\) | 1.99556e6 | 1.94080 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.09866e6 | 1.04776 | ||||||||
\(257\) | 717413. | 0.677543 | 0.338771 | − | 0.940869i | \(-0.389989\pi\) | ||||
0.338771 | + | 0.940869i | \(0.389989\pi\) | |||||||
\(258\) | 718017. | 0.671561 | ||||||||
\(259\) | 1.59696e6 | 1.47926 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 139333. | 0.126606 | ||||||||
\(262\) | −298903. | −0.269015 | ||||||||
\(263\) | 1.90624e6 | 1.69937 | 0.849685 | − | 0.527290i | \(-0.176792\pi\) | ||||
0.849685 | + | 0.527290i | \(0.176792\pi\) | |||||||
\(264\) | −138497. | −0.122301 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.08871e6 | 0.943424 | ||||||||
\(267\) | −301255. | −0.258617 | ||||||||
\(268\) | −35137.4 | −0.0298836 | ||||||||
\(269\) | 1.80790e6 | 1.52333 | 0.761665 | − | 0.647971i | \(-0.224382\pi\) | ||||
0.761665 | + | 0.647971i | \(0.224382\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.27169e6 | 1.05186 | 0.525929 | − | 0.850529i | \(-0.323718\pi\) | ||||
0.525929 | + | 0.850529i | \(0.323718\pi\) | |||||||
\(272\) | −1.69736e6 | −1.39108 | ||||||||
\(273\) | 1.24922e6 | 1.01446 | ||||||||
\(274\) | 1.29606e6 | 1.04292 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 197893. | 0.156371 | ||||||||
\(277\) | −1.80095e6 | −1.41027 | −0.705134 | − | 0.709074i | \(-0.749113\pi\) | ||||
−0.705134 | + | 0.709074i | \(0.749113\pi\) | |||||||
\(278\) | 304020. | 0.235934 | ||||||||
\(279\) | 627096. | 0.482307 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.54030e6 | 1.16370 | 0.581849 | − | 0.813297i | \(-0.302330\pi\) | ||||
0.581849 | + | 0.813297i | \(0.302330\pi\) | |||||||
\(282\) | −1.24248e6 | −0.930394 | ||||||||
\(283\) | 1.87910e6 | 1.39471 | 0.697354 | − | 0.716727i | \(-0.254360\pi\) | ||||
0.697354 | + | 0.716727i | \(0.254360\pi\) | |||||||
\(284\) | 172446. | 0.126869 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 636277. | 0.459972 | ||||||||
\(287\) | 2.45132e6 | 1.75669 | ||||||||
\(288\) | 361543. | 0.256849 | ||||||||
\(289\) | 362696. | 0.255445 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.51674e6 | −1.04998 | ||||||||
\(292\) | 485969. | 0.333543 | ||||||||
\(293\) | 307140. | 0.209010 | 0.104505 | − | 0.994524i | \(-0.466674\pi\) | ||||
0.104505 | + | 0.994524i | \(0.466674\pi\) | |||||||
\(294\) | −880944. | −0.594401 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.14634e6 | 0.760471 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | 3.09607e6 | 2.01962 | ||||||||
\(299\) | 1.31977e6 | 0.853727 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.10586e6 | −1.33971 | ||||||||
\(302\) | 2.39296e6 | 1.50980 | ||||||||
\(303\) | 1.58593e6 | 0.992379 | ||||||||
\(304\) | 1.16388e6 | 0.722311 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −725881. | −0.443161 | ||||||||
\(307\) | 1.32237e6 | 0.800771 | 0.400386 | − | 0.916347i | \(-0.368876\pi\) | ||||
0.400386 | + | 0.916347i | \(0.368876\pi\) | |||||||
\(308\) | −279816. | −0.168072 | ||||||||
\(309\) | 598371. | 0.356512 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.22049e6 | 1.30181 | 0.650904 | − | 0.759160i | \(-0.274390\pi\) | ||||
0.650904 | + | 0.759160i | \(0.274390\pi\) | |||||||
\(312\) | 896719. | 0.521519 | ||||||||
\(313\) | 978241. | 0.564397 | 0.282199 | − | 0.959356i | \(-0.408936\pi\) | ||||
0.282199 | + | 0.959356i | \(0.408936\pi\) | |||||||
\(314\) | −618023. | −0.353737 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −604032. | −0.340284 | ||||||||
\(317\) | 2.64915e6 | 1.48067 | 0.740335 | − | 0.672239i | \(-0.234667\pi\) | ||||
0.740335 | + | 0.672239i | \(0.234667\pi\) | |||||||
\(318\) | −210443. | −0.116699 | ||||||||
\(319\) | −208140. | −0.114519 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −784117. | −0.424735 | ||||||||
\(322\) | −2.00332e6 | −1.07674 | ||||||||
\(323\) | −1.22230e6 | −0.651885 | ||||||||
\(324\) | 85637.2 | 0.0453210 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.33815e6 | −1.73965 | ||||||||
\(327\) | 161051. | 0.0832901 | ||||||||
\(328\) | 1.75961e6 | 0.903093 | ||||||||
\(329\) | 3.64404e6 | 1.85607 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −555272. | −0.278571 | −0.139286 | − | 0.990252i | \(-0.544481\pi\) | ||||
−0.139286 | + | 0.990252i | \(0.544481\pi\) | |||||||
\(332\) | −5244.71 | −0.00261142 | ||||||||
\(333\) | 730104. | 0.360806 | ||||||||
\(334\) | −1.96621e6 | −0.964414 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.02717e6 | −0.979585 | ||||||||
\(337\) | 1.96065e6 | 0.940427 | 0.470213 | − | 0.882553i | \(-0.344177\pi\) | ||||
0.470213 | + | 0.882553i | \(0.344177\pi\) | |||||||
\(338\) | −1.62751e6 | −0.774878 | ||||||||
\(339\) | 296761. | 0.140251 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −936772. | −0.436263 | ||||||||
\(342\) | 497738. | 0.230110 | ||||||||
\(343\) | −394034. | −0.180841 | ||||||||
\(344\) | −1.51163e6 | −0.688730 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.99368e6 | 1.34436 | ||||||||
\(347\) | −899300. | −0.400942 | −0.200471 | − | 0.979700i | \(-0.564247\pi\) | ||||
−0.200471 | + | 0.979700i | \(0.564247\pi\) | |||||||
\(348\) | 202071. | 0.0894451 | ||||||||
\(349\) | 852454. | 0.374634 | 0.187317 | − | 0.982299i | \(-0.440021\pi\) | ||||
0.187317 | + | 0.982299i | \(0.440021\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 571123. | 0.247435 | ||||||||
\(352\) | −540083. | −0.232329 | ||||||||
\(353\) | 58325.4 | 0.0249127 | 0.0124564 | − | 0.999922i | \(-0.496035\pi\) | ||||
0.0124564 | + | 0.999922i | \(0.496035\pi\) | |||||||
\(354\) | 1.34249e6 | 0.569379 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −436903. | −0.182709 | ||||||||
\(357\) | 2.12892e6 | 0.884074 | ||||||||
\(358\) | 2.77929e6 | 1.14611 | ||||||||
\(359\) | 4.35963e6 | 1.78531 | 0.892654 | − | 0.450743i | \(-0.148841\pi\) | ||||
0.892654 | + | 0.450743i | \(0.148841\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.63797e6 | −0.661511 | ||||||||
\(362\) | 3.76103e6 | 1.50846 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | 1.81171e6 | 0.716698 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.46678e6 | 0.962562 | ||||||||
\(367\) | 1.51064e6 | 0.585459 | 0.292730 | − | 0.956195i | \(-0.405436\pi\) | ||||
0.292730 | + | 0.956195i | \(0.405436\pi\) | |||||||
\(368\) | −2.14164e6 | −0.824381 | ||||||||
\(369\) | 1.12070e6 | 0.428474 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 617202. | 0.232805 | ||||||||
\(372\) | 909460. | 0.340742 | ||||||||
\(373\) | −1.33021e6 | −0.495050 | −0.247525 | − | 0.968881i | \(-0.579617\pi\) | ||||
−0.247525 | + | 0.968881i | \(0.579617\pi\) | |||||||
\(374\) | 1.08434e6 | 0.400855 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.61577e6 | 0.954180 | ||||||||
\(377\) | 1.34763e6 | 0.488335 | ||||||||
\(378\) | −866927. | −0.312071 | ||||||||
\(379\) | −4.17882e6 | −1.49436 | −0.747181 | − | 0.664621i | \(-0.768593\pi\) | ||||
−0.747181 | + | 0.664621i | \(0.768593\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.67577e6 | −0.944356 | ||||||||
\(382\) | −4.83647e6 | −1.69578 | ||||||||
\(383\) | 1.31585e6 | 0.458362 | 0.229181 | − | 0.973384i | \(-0.426395\pi\) | ||||
0.229181 | + | 0.973384i | \(0.426395\pi\) | |||||||
\(384\) | −1.93322e6 | −0.669043 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.90043e6 | −0.990818 | ||||||||
\(387\) | −962760. | −0.326769 | ||||||||
\(388\) | −2.19969e6 | −0.741792 | ||||||||
\(389\) | −2.78879e6 | −0.934420 | −0.467210 | − | 0.884146i | \(-0.654741\pi\) | ||||
−0.467210 | + | 0.884146i | \(0.654741\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.24914e6 | 0.744003 | ||||||||
\(392\) | 1.85464e6 | 0.609598 | ||||||||
\(393\) | 400787. | 0.130898 | ||||||||
\(394\) | 5.27948e6 | 1.71337 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −127927. | −0.0409944 | ||||||||
\(397\) | 265601. | 0.0845772 | 0.0422886 | − | 0.999105i | \(-0.486535\pi\) | ||||
0.0422886 | + | 0.999105i | \(0.486535\pi\) | |||||||
\(398\) | −1.90768e6 | −0.603667 | ||||||||
\(399\) | −1.45980e6 | −0.459052 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −69100.4 | −0.0214595 | −0.0107298 | − | 0.999942i | \(-0.503415\pi\) | ||||
−0.0107298 | + | 0.999942i | \(0.503415\pi\) | |||||||
\(402\) | 162622. | 0.0501896 | ||||||||
\(403\) | 6.06528e6 | 1.86032 | ||||||||
\(404\) | 2.30003e6 | 0.701101 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.04562e6 | −0.615899 | ||||||||
\(407\) | −1.09065e6 | −0.326362 | ||||||||
\(408\) | 1.52818e6 | 0.454491 | ||||||||
\(409\) | −5.05776e6 | −1.49503 | −0.747515 | − | 0.664244i | \(-0.768753\pi\) | ||||
−0.747515 | + | 0.664244i | \(0.768753\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.73784e6 | −0.507464 | ||||||||
\(412\) | 867801. | 0.251870 | ||||||||
\(413\) | −3.93735e6 | −1.13587 | ||||||||
\(414\) | −915882. | −0.262627 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.49685e6 | 0.990703 | ||||||||
\(417\) | −407648. | −0.114801 | ||||||||
\(418\) | −743534. | −0.208142 | ||||||||
\(419\) | −4.26079e6 | −1.18565 | −0.592824 | − | 0.805332i | \(-0.701987\pi\) | ||||
−0.592824 | + | 0.805332i | \(0.701987\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.24929e6 | −1.71840 | −0.859202 | − | 0.511636i | \(-0.829040\pi\) | ||||
−0.859202 | + | 0.511636i | \(0.829040\pi\) | |||||||
\(422\) | −6.95428e6 | −1.90095 | ||||||||
\(423\) | 1.66599e6 | 0.452712 | ||||||||
\(424\) | 443041. | 0.119682 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −798108. | −0.213078 | ||||||||
\(427\) | −7.23477e6 | −1.92024 | ||||||||
\(428\) | −1.13718e6 | −0.300069 | ||||||||
\(429\) | −853159. | −0.223814 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.70549e6 | 0.442238 | 0.221119 | − | 0.975247i | \(-0.429029\pi\) | ||||
0.221119 | + | 0.975247i | \(0.429029\pi\) | |||||||
\(432\) | −926786. | −0.238930 | ||||||||
\(433\) | 605782. | 0.155273 | 0.0776367 | − | 0.996982i | \(-0.475263\pi\) | ||||
0.0776367 | + | 0.996982i | \(0.475263\pi\) | |||||||
\(434\) | −9.20669e6 | −2.34628 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 233568. | 0.0588432 | ||||||||
\(437\) | −1.54224e6 | −0.386321 | ||||||||
\(438\) | −2.24915e6 | −0.560186 | ||||||||
\(439\) | −2.77526e6 | −0.687293 | −0.343647 | − | 0.939099i | \(-0.611662\pi\) | ||||
−0.343647 | + | 0.939099i | \(0.611662\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.18122e6 | 0.289224 | ||||||||
\(442\) | −7.02073e6 | −1.70933 | ||||||||
\(443\) | 394928. | 0.0956111 | 0.0478055 | − | 0.998857i | \(-0.484777\pi\) | ||||
0.0478055 | + | 0.998857i | \(0.484777\pi\) | |||||||
\(444\) | 1.05885e6 | 0.254904 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 7.60744e6 | 1.81093 | ||||||||
\(447\) | −4.15139e6 | −0.982709 | ||||||||
\(448\) | 1.89973e6 | 0.447196 | ||||||||
\(449\) | 7.55318e6 | 1.76813 | 0.884064 | − | 0.467366i | \(-0.154797\pi\) | ||||
0.884064 | + | 0.467366i | \(0.154797\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.67413e6 | −0.387569 | ||||||||
\(452\) | 430384. | 0.0990854 | ||||||||
\(453\) | −3.20863e6 | −0.734639 | ||||||||
\(454\) | −4.57244e6 | −1.04114 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.04788e6 | −0.235993 | ||||||||
\(457\) | 2.81470e6 | 0.630436 | 0.315218 | − | 0.949019i | \(-0.397922\pi\) | ||||
0.315218 | + | 0.949019i | \(0.397922\pi\) | |||||||
\(458\) | 4.16611e6 | 0.928041 | ||||||||
\(459\) | 973305. | 0.215634 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.15222e6 | 0.252512 | 0.126256 | − | 0.991998i | \(-0.459704\pi\) | ||||
0.126256 | + | 0.991998i | \(0.459704\pi\) | |||||||
\(462\) | 1.29504e6 | 0.282278 | ||||||||
\(463\) | −2.64702e6 | −0.573857 | −0.286929 | − | 0.957952i | \(-0.592634\pi\) | ||||
−0.286929 | + | 0.957952i | \(0.592634\pi\) | |||||||
\(464\) | −2.18686e6 | −0.471549 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −210683. | −0.0449432 | ||||||||
\(467\) | 8.05020e6 | 1.70810 | 0.854052 | − | 0.520188i | \(-0.174138\pi\) | ||||
0.854052 | + | 0.520188i | \(0.174138\pi\) | |||||||
\(468\) | 828284. | 0.174809 | ||||||||
\(469\) | −476950. | −0.100125 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 828682. | 0.172122 | ||||||||
\(472\) | −2.82631e6 | −0.583936 | ||||||||
\(473\) | 1.43820e6 | 0.295574 | ||||||||
\(474\) | 2.79556e6 | 0.571509 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.08751e6 | 0.624585 | ||||||||
\(477\) | 282174. | 0.0567834 | ||||||||
\(478\) | 1.31463e6 | 0.263168 | ||||||||
\(479\) | 2.33516e6 | 0.465026 | 0.232513 | − | 0.972593i | \(-0.425305\pi\) | ||||
0.232513 | + | 0.972593i | \(0.425305\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.06157e6 | 1.39168 | ||||||||
\(482\) | 8.95191e6 | 1.75509 | ||||||||
\(483\) | 2.68617e6 | 0.523921 | ||||||||
\(484\) | 191101. | 0.0370808 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −396344. | −0.0761169 | ||||||||
\(487\) | −8.09784e6 | −1.54720 | −0.773600 | − | 0.633674i | \(-0.781546\pi\) | ||||
−0.773600 | + | 0.633674i | \(0.781546\pi\) | |||||||
\(488\) | −5.19328e6 | −0.987170 | ||||||||
\(489\) | 4.47599e6 | 0.846481 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.53902e6 | 1.03688 | 0.518441 | − | 0.855114i | \(-0.326513\pi\) | ||||
0.518441 | + | 0.855114i | \(0.326513\pi\) | |||||||
\(492\) | 1.62532e6 | 0.302710 | ||||||||
\(493\) | 2.29663e6 | 0.425573 | ||||||||
\(494\) | 4.81413e6 | 0.887565 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.84240e6 | −1.79637 | ||||||||
\(497\) | 2.34075e6 | 0.425074 | ||||||||
\(498\) | 24273.4 | 0.00438589 | ||||||||
\(499\) | −1.00373e7 | −1.80454 | −0.902271 | − | 0.431169i | \(-0.858101\pi\) | ||||
−0.902271 | + | 0.431169i | \(0.858101\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.63641e6 | 0.469266 | ||||||||
\(502\) | 658670. | 0.116656 | ||||||||
\(503\) | −2.38538e6 | −0.420376 | −0.210188 | − | 0.977661i | \(-0.567408\pi\) | ||||
−0.210188 | + | 0.977661i | \(0.567408\pi\) | |||||||
\(504\) | 1.82513e6 | 0.320049 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.36817e6 | 0.237555 | ||||||||
\(507\) | 2.18227e6 | 0.377041 | ||||||||
\(508\) | −3.88059e6 | −0.667173 | ||||||||
\(509\) | −8.86436e6 | −1.51654 | −0.758268 | − | 0.651943i | \(-0.773954\pi\) | ||||
−0.758268 | + | 0.651943i | \(0.773954\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.59647e6 | 1.11753 | ||||||||
\(512\) | −500636. | −0.0844009 | ||||||||
\(513\) | −667396. | −0.111967 | ||||||||
\(514\) | −4.81536e6 | −0.803935 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.39626e6 | −0.230857 | ||||||||
\(517\) | −2.48870e6 | −0.409493 | ||||||||
\(518\) | −1.07190e7 | −1.75521 | ||||||||
\(519\) | −4.01411e6 | −0.654140 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.39366e6 | 0.870542 | 0.435271 | − | 0.900300i | \(-0.356653\pi\) | ||||
0.435271 | + | 0.900300i | \(0.356653\pi\) | |||||||
\(522\) | −935220. | −0.150223 | ||||||||
\(523\) | −850386. | −0.135945 | −0.0679723 | − | 0.997687i | \(-0.521653\pi\) | ||||
−0.0679723 | + | 0.997687i | \(0.521653\pi\) | |||||||
\(524\) | 581250. | 0.0924773 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.27949e7 | −2.01638 | ||||||||
\(527\) | 1.03364e7 | 1.62123 | ||||||||
\(528\) | 1.38446e6 | 0.216120 | ||||||||
\(529\) | −3.59849e6 | −0.559089 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.80008e6 | −0.277049 | ||||||||
\(532\) | −2.11711e6 | −0.324313 | ||||||||
\(533\) | 1.08394e7 | 1.65268 | ||||||||
\(534\) | 2.02206e6 | 0.306860 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −342365. | −0.0514728 | ||||||||
\(537\) | −3.72664e6 | −0.557675 | ||||||||
\(538\) | −1.21348e7 | −1.80750 | ||||||||
\(539\) | −1.76454e6 | −0.261613 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.13219e6 | 1.04768 | 0.523841 | − | 0.851816i | \(-0.324499\pi\) | ||||
0.523841 | + | 0.851816i | \(0.324499\pi\) | |||||||
\(542\) | −8.53570e6 | −1.24808 | ||||||||
\(543\) | −5.04301e6 | −0.733990 | ||||||||
\(544\) | 5.95931e6 | 0.863374 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.38492e6 | −1.20370 | ||||||||
\(547\) | 1.39768e6 | 0.199729 | 0.0998644 | − | 0.995001i | \(-0.468159\pi\) | ||||
0.0998644 | + | 0.995001i | \(0.468159\pi\) | |||||||
\(548\) | −2.52034e6 | −0.358515 | ||||||||
\(549\) | −3.30761e6 | −0.468364 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.57480e6 | −0.220977 | ||||||||
\(552\) | 1.92819e6 | 0.269341 | ||||||||
\(553\) | −8.19904e6 | −1.14012 | ||||||||
\(554\) | 1.20882e7 | 1.67335 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −591201. | −0.0811052 | ||||||||
\(557\) | −1.91000e6 | −0.260852 | −0.130426 | − | 0.991458i | \(-0.541635\pi\) | ||||
−0.130426 | + | 0.991458i | \(0.541635\pi\) | |||||||
\(558\) | −4.20914e6 | −0.572279 | ||||||||
\(559\) | −9.31183e6 | −1.26039 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.45395e6 | −0.195048 | ||||||||
\(562\) | −1.03387e7 | −1.38078 | ||||||||
\(563\) | −1.33043e7 | −1.76898 | −0.884488 | − | 0.466563i | \(-0.845492\pi\) | ||||
−0.884488 | + | 0.466563i | \(0.845492\pi\) | |||||||
\(564\) | 2.41614e6 | 0.319834 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.26127e7 | −1.65488 | ||||||||
\(567\) | 1.16243e6 | 0.151848 | ||||||||
\(568\) | 1.68024e6 | 0.218525 | ||||||||
\(569\) | 692234. | 0.0896339 | 0.0448170 | − | 0.998995i | \(-0.485730\pi\) | ||||
0.0448170 | + | 0.998995i | \(0.485730\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.25834e6 | 0.931638 | 0.465819 | − | 0.884880i | \(-0.345760\pi\) | ||||
0.465819 | + | 0.884880i | \(0.345760\pi\) | |||||||
\(572\) | −1.23731e6 | −0.158121 | ||||||||
\(573\) | 6.48503e6 | 0.825136 | ||||||||
\(574\) | −1.64536e7 | −2.08439 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 868524. | 0.109075 | ||||||||
\(577\) | 1.41479e7 | 1.76910 | 0.884550 | − | 0.466446i | \(-0.154466\pi\) | ||||
0.884550 | + | 0.466446i | \(0.154466\pi\) | |||||||
\(578\) | −2.43446e6 | −0.303098 | ||||||||
\(579\) | 3.88907e6 | 0.482113 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −71190.9 | −0.00874952 | ||||||||
\(582\) | 1.01805e7 | 1.24584 | ||||||||
\(583\) | −421519. | −0.0513625 | ||||||||
\(584\) | 4.73509e6 | 0.574508 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.06156e6 | −0.248000 | ||||||||
\(587\) | −5.01437e6 | −0.600649 | −0.300325 | − | 0.953837i | \(-0.597095\pi\) | ||||
−0.300325 | + | 0.953837i | \(0.597095\pi\) | |||||||
\(588\) | 1.71309e6 | 0.204333 | ||||||||
\(589\) | −7.08769e6 | −0.841815 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.07904e6 | −0.833692 | ||||||||
\(592\) | −1.14591e7 | −1.34384 | ||||||||
\(593\) | 6.71458e6 | 0.784119 | 0.392060 | − | 0.919940i | \(-0.371763\pi\) | ||||
0.392060 | + | 0.919940i | \(0.371763\pi\) | |||||||
\(594\) | 592069. | 0.0688503 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.02065e6 | −0.694269 | ||||||||
\(597\) | 2.55793e6 | 0.293733 | ||||||||
\(598\) | −8.85842e6 | −1.01299 | ||||||||
\(599\) | −1.12021e7 | −1.27565 | −0.637825 | − | 0.770182i | \(-0.720166\pi\) | ||||
−0.637825 | + | 0.770182i | \(0.720166\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.05901e7 | 1.19596 | 0.597978 | − | 0.801512i | \(-0.295971\pi\) | ||||
0.597978 | + | 0.801512i | \(0.295971\pi\) | |||||||
\(602\) | 1.41347e7 | 1.58963 | ||||||||
\(603\) | −218053. | −0.0244213 | ||||||||
\(604\) | −4.65339e6 | −0.519011 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.06449e7 | −1.17750 | ||||||||
\(607\) | −1.39277e7 | −1.53429 | −0.767147 | − | 0.641472i | \(-0.778324\pi\) | ||||
−0.767147 | + | 0.641472i | \(0.778324\pi\) | |||||||
\(608\) | −4.08631e6 | −0.448303 | ||||||||
\(609\) | 2.74289e6 | 0.299685 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.61135e7 | 1.74617 | ||||||||
\(612\) | 1.41156e6 | 0.152342 | ||||||||
\(613\) | −1.91560e6 | −0.205898 | −0.102949 | − | 0.994687i | \(-0.532828\pi\) | ||||
−0.102949 | + | 0.994687i | \(0.532828\pi\) | |||||||
\(614\) | −8.87592e6 | −0.950151 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.72642e6 | −0.289495 | ||||||||
\(617\) | 524280. | 0.0554435 | 0.0277217 | − | 0.999616i | \(-0.491175\pi\) | ||||
0.0277217 | + | 0.999616i | \(0.491175\pi\) | |||||||
\(618\) | −4.01633e6 | −0.423018 | ||||||||
\(619\) | 9.20908e6 | 0.966028 | 0.483014 | − | 0.875613i | \(-0.339542\pi\) | ||||
0.483014 | + | 0.875613i | \(0.339542\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.22807e6 | 0.127789 | ||||||||
\(622\) | −1.49042e7 | −1.54465 | ||||||||
\(623\) | −5.93045e6 | −0.612164 | ||||||||
\(624\) | −8.96389e6 | −0.921584 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.56606e6 | −0.669683 | ||||||||
\(627\) | 996975. | 0.101278 | ||||||||
\(628\) | 1.20182e6 | 0.121601 | ||||||||
\(629\) | 1.20343e7 | 1.21281 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.98666e6 | 0.198633 | 0.0993164 | − | 0.995056i | \(-0.468334\pi\) | ||||
0.0993164 | + | 0.995056i | \(0.468334\pi\) | |||||||
\(632\) | −5.88545e6 | −0.586121 | ||||||||
\(633\) | 9.32471e6 | 0.924967 | ||||||||
\(634\) | −1.77814e7 | −1.75688 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 409229. | 0.0401166 | ||||||||
\(637\) | 1.14248e7 | 1.11558 | ||||||||
\(638\) | 1.39706e6 | 0.135882 | ||||||||
\(639\) | 1.07015e6 | 0.103680 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.31651e7 | −1.26555 | −0.632776 | − | 0.774335i | \(-0.718085\pi\) | ||||
−0.632776 | + | 0.774335i | \(0.718085\pi\) | |||||||
\(642\) | 5.26308e6 | 0.503967 | ||||||||
\(643\) | −7.46182e6 | −0.711733 | −0.355867 | − | 0.934537i | \(-0.615814\pi\) | ||||
−0.355867 | + | 0.934537i | \(0.615814\pi\) | |||||||
\(644\) | 3.89568e6 | 0.370142 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 8.20421e6 | 0.773491 | ||||||||
\(647\) | −1.12027e7 | −1.05212 | −0.526058 | − | 0.850449i | \(-0.676331\pi\) | ||||
−0.526058 | + | 0.850449i | \(0.676331\pi\) | |||||||
\(648\) | 834415. | 0.0780629 | ||||||||
\(649\) | 2.68902e6 | 0.250600 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.23449e7 | 1.14165 | ||||||||
\(652\) | 6.49141e6 | 0.598026 | ||||||||
\(653\) | 5.01727e6 | 0.460452 | 0.230226 | − | 0.973137i | \(-0.426053\pi\) | ||||
0.230226 | + | 0.973137i | \(0.426053\pi\) | |||||||
\(654\) | −1.08099e6 | −0.0988275 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.75896e7 | −1.59587 | ||||||||
\(657\) | 3.01579e6 | 0.272576 | ||||||||
\(658\) | −2.44592e7 | −2.20231 | ||||||||
\(659\) | 1.59087e6 | 0.142699 | 0.0713495 | − | 0.997451i | \(-0.477269\pi\) | ||||
0.0713495 | + | 0.997451i | \(0.477269\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.38029e7 | 1.22876 | 0.614378 | − | 0.789012i | \(-0.289407\pi\) | ||||
0.614378 | + | 0.789012i | \(0.289407\pi\) | |||||||
\(662\) | 3.72705e6 | 0.330537 | ||||||||
\(663\) | 9.41381e6 | 0.831729 | ||||||||
\(664\) | −51102.4 | −0.00449802 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.90054e6 | −0.428113 | ||||||||
\(667\) | 2.89778e6 | 0.252203 | ||||||||
\(668\) | 3.82351e6 | 0.331529 | ||||||||
\(669\) | −1.02005e7 | −0.881163 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.94100e6 | 0.423651 | ||||||||
\(672\) | 7.11726e6 | 0.607980 | ||||||||
\(673\) | 1.14669e7 | 0.975911 | 0.487955 | − | 0.872869i | \(-0.337743\pi\) | ||||
0.487955 | + | 0.872869i | \(0.337743\pi\) | |||||||
\(674\) | −1.31601e7 | −1.11586 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.16488e6 | 0.266374 | ||||||||
\(677\) | 1.82188e7 | 1.52774 | 0.763869 | − | 0.645371i | \(-0.223297\pi\) | ||||
0.763869 | + | 0.645371i | \(0.223297\pi\) | |||||||
\(678\) | −1.99189e6 | −0.166414 | ||||||||
\(679\) | −2.98583e7 | −2.48536 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.13100e6 | 0.506598 | ||||||||
\(682\) | 6.28772e6 | 0.517645 | ||||||||
\(683\) | −1.75425e7 | −1.43893 | −0.719464 | − | 0.694530i | \(-0.755612\pi\) | ||||
−0.719464 | + | 0.694530i | \(0.755612\pi\) | |||||||
\(684\) | −967907. | −0.0791031 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.64480e6 | 0.214577 | ||||||||
\(687\) | −5.58617e6 | −0.451567 | ||||||||
\(688\) | 1.51107e7 | 1.21707 | ||||||||
\(689\) | 2.72919e6 | 0.219021 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.62835e6 | 0.607765 | 0.303882 | − | 0.952710i | \(-0.401717\pi\) | ||||
0.303882 | + | 0.952710i | \(0.401717\pi\) | |||||||
\(692\) | −5.82155e6 | −0.462140 | ||||||||
\(693\) | −1.73646e6 | −0.137351 | ||||||||
\(694\) | 6.03621e6 | 0.475735 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.96890e6 | 0.154064 | ||||||||
\(697\) | 1.84725e7 | 1.44027 | ||||||||
\(698\) | −5.72177e6 | −0.444520 | ||||||||
\(699\) | 282496. | 0.0218685 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.99597e7 | −1.53412 | −0.767059 | − | 0.641577i | \(-0.778281\pi\) | ||||
−0.767059 | + | 0.641577i | \(0.778281\pi\) | |||||||
\(702\) | −3.83344e6 | −0.293593 | ||||||||
\(703\) | −8.25194e6 | −0.629749 | ||||||||
\(704\) | −1.29743e6 | −0.0986622 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −391487. | −0.0295601 | ||||||||
\(707\) | 3.12203e7 | 2.34903 | ||||||||
\(708\) | −2.61061e6 | −0.195731 | ||||||||
\(709\) | 8.79537e6 | 0.657110 | 0.328555 | − | 0.944485i | \(-0.393438\pi\) | ||||
0.328555 | + | 0.944485i | \(0.393438\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.74846e6 | −0.278086 | ||||||||
\(712\) | −4.25701e6 | −0.314706 | ||||||||
\(713\) | 1.30420e7 | 0.960771 | ||||||||
\(714\) | −1.42895e7 | −1.04899 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.40464e6 | −0.393989 | ||||||||
\(717\) | −1.76273e6 | −0.128053 | ||||||||
\(718\) | −2.92623e7 | −2.11835 | ||||||||
\(719\) | −1.04268e7 | −0.752190 | −0.376095 | − | 0.926581i | \(-0.622733\pi\) | ||||
−0.376095 | + | 0.926581i | \(0.622733\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.17794e7 | 0.843889 | ||||||||
\(722\) | 1.09942e7 | 0.784913 | ||||||||
\(723\) | −1.20033e7 | −0.853991 | ||||||||
\(724\) | −7.31374e6 | −0.518553 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −884448. | −0.0622775 | ||||||||
\(727\) | −3.28724e6 | −0.230672 | −0.115336 | − | 0.993327i | \(-0.536795\pi\) | ||||
−0.115336 | + | 0.993327i | \(0.536795\pi\) | |||||||
\(728\) | 1.76526e7 | 1.23447 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.58692e7 | −1.09840 | ||||||||
\(732\) | −4.79694e6 | −0.330892 | ||||||||
\(733\) | 5.45350e6 | 0.374900 | 0.187450 | − | 0.982274i | \(-0.439978\pi\) | ||||
0.187450 | + | 0.982274i | \(0.439978\pi\) | |||||||
\(734\) | −1.01396e7 | −0.694674 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.51917e6 | 0.511653 | ||||||||
\(737\) | 325734. | 0.0220899 | ||||||||
\(738\) | −7.52227e6 | −0.508403 | ||||||||
\(739\) | 2.58376e7 | 1.74037 | 0.870183 | − | 0.492729i | \(-0.164001\pi\) | ||||
0.870183 | + | 0.492729i | \(0.164001\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.45507e6 | −0.431872 | ||||||||
\(742\) | −4.14273e6 | −0.276234 | ||||||||
\(743\) | −7.94543e6 | −0.528014 | −0.264007 | − | 0.964521i | \(-0.585044\pi\) | ||||
−0.264007 | + | 0.964521i | \(0.585044\pi\) | |||||||
\(744\) | 8.86142e6 | 0.586909 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.92854e6 | 0.587399 | ||||||||
\(747\) | −32547.2 | −0.00213409 | ||||||||
\(748\) | −2.10862e6 | −0.137799 | ||||||||
\(749\) | −1.54360e7 | −1.00538 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.16319e7 | 0.752574 | 0.376287 | − | 0.926503i | \(-0.377201\pi\) | ||||
0.376287 | + | 0.926503i | \(0.377201\pi\) | |||||||
\(752\) | −2.61481e7 | −1.68615 | ||||||||
\(753\) | −883184. | −0.0567628 | ||||||||
\(754\) | −9.04546e6 | −0.579432 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.68584e6 | 0.107278 | ||||||||
\(757\) | −1.46923e7 | −0.931856 | −0.465928 | − | 0.884823i | \(-0.654279\pi\) | ||||
−0.465928 | + | 0.884823i | \(0.654279\pi\) | |||||||
\(758\) | 2.80487e7 | 1.77313 | ||||||||
\(759\) | −1.83452e6 | −0.115590 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.52759e6 | −0.0956194 | −0.0478097 | − | 0.998856i | \(-0.515224\pi\) | ||||
−0.0478097 | + | 0.998856i | \(0.515224\pi\) | |||||||
\(762\) | 1.79600e7 | 1.12052 | ||||||||
\(763\) | 3.17041e6 | 0.197154 | ||||||||
\(764\) | 9.40507e6 | 0.582946 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.83212e6 | −0.543867 | ||||||||
\(767\) | −1.74104e7 | −1.06862 | ||||||||
\(768\) | 9.88792e6 | 0.604926 | ||||||||
\(769\) | 1.53066e7 | 0.933389 | 0.466694 | − | 0.884419i | \(-0.345445\pi\) | ||||
0.466694 | + | 0.884419i | \(0.345445\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.45672e6 | 0.391180 | ||||||||
\(772\) | 5.64021e6 | 0.340606 | ||||||||
\(773\) | 2.13061e7 | 1.28249 | 0.641245 | − | 0.767336i | \(-0.278418\pi\) | ||||
0.641245 | + | 0.767336i | \(0.278418\pi\) | |||||||
\(774\) | 6.46215e6 | 0.387726 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.14329e7 | −1.27769 | ||||||||
\(777\) | 1.43727e7 | 0.854054 | ||||||||
\(778\) | 1.87187e7 | 1.10873 | ||||||||
\(779\) | −1.26666e7 | −0.747855 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.59862e6 | −0.0937817 | ||||||||
\(782\) | −1.50965e7 | −0.882793 | ||||||||
\(783\) | 1.25400e6 | 0.0730959 | ||||||||
\(784\) | −1.85395e7 | −1.07723 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.69013e6 | −0.155316 | ||||||||
\(787\) | −1.60779e7 | −0.925319 | −0.462659 | − | 0.886536i | \(-0.653105\pi\) | ||||
−0.462659 | + | 0.886536i | \(0.653105\pi\) | |||||||
\(788\) | −1.02665e7 | −0.588991 | ||||||||
\(789\) | 1.71562e7 | 0.981132 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.84197e6 | 0.331985 | ||||||||
\(792\) | −1.24647e6 | −0.0706105 | ||||||||
\(793\) | −3.19913e7 | −1.80654 | ||||||||
\(794\) | −1.78274e6 | −0.100355 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.70970e6 | 0.207518 | ||||||||
\(797\) | 3.34929e7 | 1.86770 | 0.933849 | − | 0.357668i | \(-0.116428\pi\) | ||||
0.933849 | + | 0.357668i | \(0.116428\pi\) | |||||||
\(798\) | 9.79836e6 | 0.544686 | ||||||||
\(799\) | 2.74605e7 | 1.52175 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.71130e6 | −0.149312 | ||||||||
\(802\) | 463810. | 0.0254627 | ||||||||
\(803\) | −4.50507e6 | −0.246554 | ||||||||
\(804\) | −316237. | −0.0172533 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.07108e7 | −2.20736 | ||||||||
\(807\) | 1.62711e7 | 0.879495 | ||||||||
\(808\) | 2.24106e7 | 1.20761 | ||||||||
\(809\) | −3.65008e7 | −1.96079 | −0.980396 | − | 0.197037i | \(-0.936868\pi\) | ||||
−0.980396 | + | 0.197037i | \(0.936868\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.57753e7 | −0.842222 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(812\) | 3.97793e6 | 0.211723 | ||||||||
\(813\) | 1.14452e7 | 0.607290 | ||||||||
\(814\) | 7.32056e6 | 0.387243 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.52762e7 | −0.803139 | ||||||||
\(817\) | 1.08815e7 | 0.570340 | ||||||||
\(818\) | 3.39483e7 | 1.77392 | ||||||||
\(819\) | 1.12430e7 | 0.585697 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.08891e7 | −0.563811 | −0.281906 | − | 0.959442i | \(-0.590966\pi\) | ||||
−0.281906 | + | 0.959442i | \(0.590966\pi\) | |||||||
\(822\) | 1.16646e7 | 0.602129 | ||||||||
\(823\) | 4.77752e6 | 0.245869 | 0.122934 | − | 0.992415i | \(-0.460770\pi\) | ||||
0.122934 | + | 0.992415i | \(0.460770\pi\) | |||||||
\(824\) | 8.45552e6 | 0.433832 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.64279e7 | 1.34776 | ||||||||
\(827\) | −1.24682e7 | −0.633927 | −0.316964 | − | 0.948438i | \(-0.602663\pi\) | ||||
−0.316964 | + | 0.948438i | \(0.602663\pi\) | |||||||
\(828\) | 1.78104e6 | 0.0902811 | ||||||||
\(829\) | −2.92619e7 | −1.47882 | −0.739412 | − | 0.673253i | \(-0.764897\pi\) | ||||
−0.739412 | + | 0.673253i | \(0.764897\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.62085e7 | −0.814219 | ||||||||
\(832\) | 8.40038e6 | 0.420717 | ||||||||
\(833\) | 1.94701e7 | 0.972199 | ||||||||
\(834\) | 2.73618e6 | 0.136217 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.44589e6 | 0.0715514 | ||||||||
\(837\) | 5.64386e6 | 0.278460 | ||||||||
\(838\) | 2.85989e7 | 1.40682 | ||||||||
\(839\) | 1.47124e7 | 0.721571 | 0.360786 | − | 0.932649i | \(-0.382509\pi\) | ||||
0.360786 | + | 0.932649i | \(0.382509\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.75522e7 | −0.855739 | ||||||||
\(842\) | 4.19459e7 | 2.03896 | ||||||||
\(843\) | 1.38627e7 | 0.671861 | ||||||||
\(844\) | 1.35234e7 | 0.653475 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.11823e7 | −0.537163 | ||||||||
\(847\) | 2.59398e6 | 0.124239 | ||||||||
\(848\) | −4.42878e6 | −0.211492 | ||||||||
\(849\) | 1.69119e7 | 0.805235 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.51843e7 | 0.718739 | ||||||||
\(852\) | 1.55201e6 | 0.0732480 | ||||||||
\(853\) | −4.14062e7 | −1.94846 | −0.974232 | − | 0.225548i | \(-0.927583\pi\) | ||||
−0.974232 | + | 0.225548i | \(0.927583\pi\) | |||||||
\(854\) | 4.85606e7 | 2.27845 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.10803e7 | −0.516852 | ||||||||
\(857\) | 1.96593e7 | 0.914359 | 0.457179 | − | 0.889375i | \(-0.348860\pi\) | ||||
0.457179 | + | 0.889375i | \(0.348860\pi\) | |||||||
\(858\) | 5.72650e6 | 0.265565 | ||||||||
\(859\) | 3.89269e7 | 1.79997 | 0.899987 | − | 0.435916i | \(-0.143575\pi\) | ||||
0.899987 | + | 0.435916i | \(0.143575\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.20619e7 | 1.01423 | ||||||||
\(862\) | −1.14475e7 | −0.524736 | ||||||||
\(863\) | 2.21492e7 | 1.01235 | 0.506176 | − | 0.862430i | \(-0.331059\pi\) | ||||
0.506176 | + | 0.862430i | \(0.331059\pi\) | |||||||
\(864\) | 3.25389e6 | 0.148292 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.06608e6 | −0.184239 | ||||||||
\(867\) | 3.26426e6 | 0.147482 | ||||||||
\(868\) | 1.79034e7 | 0.806561 | ||||||||
\(869\) | 5.59955e6 | 0.251538 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.10901e6 | −0.0941963 | ||||||||
\(872\) | 2.27579e6 | 0.101354 | ||||||||
\(873\) | −1.36507e7 | −0.606203 | ||||||||
\(874\) | 1.03517e7 | 0.458387 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.37372e6 | 0.192571 | ||||||||
\(877\) | −1.54661e7 | −0.679017 | −0.339509 | − | 0.940603i | \(-0.610261\pi\) | ||||
−0.339509 | + | 0.940603i | \(0.610261\pi\) | |||||||
\(878\) | 1.86278e7 | 0.815505 | ||||||||
\(879\) | 2.76426e6 | 0.120672 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.87591e7 | 1.24835 | 0.624174 | − | 0.781286i | \(-0.285436\pi\) | ||||
0.624174 | + | 0.781286i | \(0.285436\pi\) | |||||||
\(882\) | −7.92849e6 | −0.343178 | ||||||||
\(883\) | −2.15386e7 | −0.929642 | −0.464821 | − | 0.885405i | \(-0.653881\pi\) | ||||
−0.464821 | + | 0.885405i | \(0.653881\pi\) | |||||||
\(884\) | 1.36526e7 | 0.587604 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.65080e6 | −0.113447 | ||||||||
\(887\) | 2.32877e7 | 0.993844 | 0.496922 | − | 0.867795i | \(-0.334463\pi\) | ||||
0.496922 | + | 0.867795i | \(0.334463\pi\) | |||||||
\(888\) | 1.03170e7 | 0.439058 | ||||||||
\(889\) | −5.26746e7 | −2.23536 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | −1.47935e7 | −0.622529 | ||||||||
\(893\) | −1.88297e7 | −0.790161 | ||||||||
\(894\) | 2.78646e7 | 1.16603 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.80570e7 | −1.58367 | ||||||||
\(897\) | 1.18779e7 | 0.492900 | ||||||||
\(898\) | −5.06978e7 | −2.09796 | ||||||||
\(899\) | 1.33174e7 | 0.549565 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.65107e6 | 0.190872 | ||||||||
\(902\) | 1.12370e7 | 0.459868 | ||||||||
\(903\) | −1.89527e7 | −0.773485 | ||||||||
\(904\) | 4.19349e6 | 0.170669 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.15367e7 | 0.871682 | ||||||||
\(907\) | −6.21299e6 | −0.250774 | −0.125387 | − | 0.992108i | \(-0.540017\pi\) | ||||
−0.125387 | + | 0.992108i | \(0.540017\pi\) | |||||||
\(908\) | 8.89162e6 | 0.357904 | ||||||||
\(909\) | 1.42734e7 | 0.572950 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.40141e7 | 0.958674 | 0.479337 | − | 0.877631i | \(-0.340877\pi\) | ||||
0.479337 | + | 0.877631i | \(0.340877\pi\) | |||||||
\(912\) | 1.04749e7 | 0.417027 | ||||||||
\(913\) | 48620.0 | 0.00193036 | ||||||||
\(914\) | −1.88926e7 | −0.748041 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.10147e6 | −0.319025 | ||||||||
\(917\) | 7.88981e6 | 0.309844 | ||||||||
\(918\) | −6.53293e6 | −0.255859 | ||||||||
\(919\) | 1.20620e7 | 0.471117 | 0.235559 | − | 0.971860i | \(-0.424308\pi\) | ||||
0.235559 | + | 0.971860i | \(0.424308\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.19014e7 | 0.462325 | ||||||||
\(922\) | −7.73380e6 | −0.299616 | ||||||||
\(923\) | 1.03505e7 | 0.399906 | ||||||||
\(924\) | −2.51835e6 | −0.0970366 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.77671e7 | 0.680908 | ||||||||
\(927\) | 5.38534e6 | 0.205832 | ||||||||
\(928\) | 7.67794e6 | 0.292668 | ||||||||
\(929\) | 5.56585e6 | 0.211589 | 0.105794 | − | 0.994388i | \(-0.466262\pi\) | ||||
0.105794 | + | 0.994388i | \(0.466262\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.33507e7 | −0.504811 | ||||||||
\(932\) | 409696. | 0.0154498 | ||||||||
\(933\) | 1.99844e7 | 0.751600 | ||||||||
\(934\) | −5.40338e7 | −2.02674 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.07047e6 | 0.301099 | ||||||||
\(937\) | 1.39429e7 | 0.518806 | 0.259403 | − | 0.965769i | \(-0.416474\pi\) | ||||
0.259403 | + | 0.965769i | \(0.416474\pi\) | |||||||
\(938\) | 3.20134e6 | 0.118802 | ||||||||
\(939\) | 8.80417e6 | 0.325855 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.76975e7 | −0.651536 | −0.325768 | − | 0.945450i | \(-0.605623\pi\) | ||||
−0.325768 | + | 0.945450i | \(0.605623\pi\) | |||||||
\(942\) | −5.56221e6 | −0.204230 | ||||||||
\(943\) | 2.33077e7 | 0.853534 | ||||||||
\(944\) | 2.82527e7 | 1.03188 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.65334e6 | −0.350711 | ||||||||
\(947\) | −1.08090e7 | −0.391659 | −0.195830 | − | 0.980638i | \(-0.562740\pi\) | ||||
−0.195830 | + | 0.980638i | \(0.562740\pi\) | |||||||
\(948\) | −5.43629e6 | −0.196463 | ||||||||
\(949\) | 2.91688e7 | 1.05136 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.38423e7 | 0.854865 | ||||||||
\(952\) | 3.00835e7 | 1.07581 | ||||||||
\(953\) | −2.79930e7 | −0.998428 | −0.499214 | − | 0.866479i | \(-0.666378\pi\) | ||||
−0.499214 | + | 0.866479i | \(0.666378\pi\) | |||||||
\(954\) | −1.89398e6 | −0.0673760 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.55644e6 | −0.0904673 | ||||||||
\(957\) | −1.87326e6 | −0.0661177 | ||||||||
\(958\) | −1.56738e7 | −0.551775 | ||||||||
\(959\) | −3.42108e7 | −1.20120 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.13082e7 | 1.09358 | ||||||||
\(962\) | −4.73981e7 | −1.65129 | ||||||||
\(963\) | −7.05705e6 | −0.245221 | ||||||||
\(964\) | −1.74080e7 | −0.603332 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.80299e7 | −0.621655 | ||||||||
\(967\) | −3.30769e7 | −1.13752 | −0.568760 | − | 0.822504i | \(-0.692577\pi\) | ||||
−0.568760 | + | 0.822504i | \(0.692577\pi\) | |||||||
\(968\) | 1.86201e6 | 0.0638696 | ||||||||
\(969\) | −1.10007e7 | −0.376366 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.56721e7 | −1.21417 | −0.607086 | − | 0.794636i | \(-0.707662\pi\) | ||||
−0.607086 | + | 0.794636i | \(0.707662\pi\) | |||||||
\(972\) | 770735. | 0.0261661 | ||||||||
\(973\) | −8.02488e6 | −0.271742 | ||||||||
\(974\) | 5.43536e7 | 1.83582 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.19137e7 | 1.74444 | ||||||||
\(977\) | −4.13863e7 | −1.38714 | −0.693571 | − | 0.720389i | \(-0.743963\pi\) | ||||
−0.693571 | + | 0.720389i | \(0.743963\pi\) | |||||||
\(978\) | −3.00434e7 | −1.00439 | ||||||||
\(979\) | 4.05021e6 | 0.135058 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.44946e6 | 0.0480876 | ||||||||
\(982\) | −3.71785e7 | −1.23031 | ||||||||
\(983\) | −2.54427e7 | −0.839805 | −0.419903 | − | 0.907569i | \(-0.637936\pi\) | ||||
−0.419903 | + | 0.907569i | \(0.637936\pi\) | |||||||
\(984\) | 1.58365e7 | 0.521401 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.54152e7 | −0.504961 | ||||||||
\(987\) | 3.27964e7 | 1.07160 | ||||||||
\(988\) | −9.36161e6 | −0.305111 | ||||||||
\(989\) | −2.00230e7 | −0.650935 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.30502e7 | 0.745573 | 0.372786 | − | 0.927917i | \(-0.378402\pi\) | ||||
0.372786 | + | 0.927917i | \(0.378402\pi\) | |||||||
\(992\) | 3.45560e7 | 1.11492 | ||||||||
\(993\) | −4.99745e6 | −0.160833 | ||||||||
\(994\) | −1.57114e7 | −0.504370 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −47202.4 | −0.00150770 | ||||||||
\(997\) | −1.12684e7 | −0.359026 | −0.179513 | − | 0.983756i | \(-0.557452\pi\) | ||||
−0.179513 | + | 0.983756i | \(0.557452\pi\) | |||||||
\(998\) | 6.73717e7 | 2.14117 | ||||||||
\(999\) | 6.57093e6 | 0.208312 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 825.6.a.r.1.3 | ✓ | 9 | |
5.4 | even | 2 | 825.6.a.s.1.7 | yes | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.r.1.3 | ✓ | 9 | 1.1 | even | 1 | trivial | |
825.6.a.s.1.7 | yes | 9 | 5.4 | even | 2 |